Limit theorems for radial random walks on Euclidean spaces of high dimensions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1319.60042
DOI: 10.1017/S144678871400024X
author: Waldemar Grundmann
published in: Journal of the Australian Mathematical Society
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1210.7090
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 6357665
zbMATH Keywords: radial random walks
zbMATH Keywords: central limit theorems
zbMATH Keywords: Euclidean spaces
MaRDI profile type: Publication
arXiv ID: 1210.7090
cites work: A new class of matrix variate elliptically contoured distributions
cites work: Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces
cites work: Dependence of the Berry-Esseen estimate on the dimension
cites work: Central limit theorems for radial random walks on \(p \times q\) matrices for \(p \to \infty\)
cites work: Bessel functions of matrix argument
cites work: Enumerative combinatorics. Volume 2.
cites work: Limit theorems for radial random walks on p × q-matrices as p tends to infinity
cites work: Spaces with an abstract convolution of measures
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title: Limit theorems for radial random walks on Euclidean spaces of high dimensions
review text: The paper presents a central limit theorem (CLT) for norms of random walks provided that the length \(n\) and dimension \(p_n\) of the random walks are growing to infinity. The asymptotics of the ratio \(\frac{n}{p_n}\) lead to two different cases of the CLT. The limits are Gaussian in both cases.
reviewed by: Petr Lachout
description: scientific article; zbMATH DE number 6357665